Exact Enumeration and Sampling of Matrices with Specified Margins

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling

Exact sampling and counting for fixed-margin matrices

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1131 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1104.032

Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).Comment: This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.270

“Double Jeopardy for $1000 Alex” - What It Is and How to Apply It

PresentationProcess hazards analyses, such as Hazard and Operability studies (HAZOPs) and Layer of Protection Analyses (LOPAs), are structured, team-based exercises focused on hazard identification, risk assessment, and risk management. In order to manage the complexity associated with these analyses, recognized and generally accepted rules are imposed to manage and limit the review of hazard scenarios involving simultaneous failures. One of these rules has been dubbed “double jeopardy”. Based on the authors experience via direct observation and review of PHA documentation, PHA teams continue to struggle to understand double jeopardy and how to effectively address simultaneous failures when applying PHA methodologies, such as HAZOP and LOPA. In addition, more widely accepted emergence and use of enabling conditions and conditional modifiers when developing hazard scenarios has blurred the legacy definition of double jeopardy. In this paper, the authors provide an overview of double jeopardy along with specific PHA examples regarding credible as well as inappropriate applications of double jeopardy. They also present tools and recommendations to enhance PHA teams’ performances regarding the application of double jeopardy. More specifically, they address issues regarding latent failures (revealed vs. unrevealed conditions), concurrent incidence of failures, and independence of initiating events. The target audience for this paper is anyone whose responsibilities include (1) leading within an organization that uses PHAs, (2) establishing PHA guidance documents, (3) applying PHA methodologies, and (4) reviewing PHA outputs and reports

Multitissue molecular, genomic, and developmental effects of the deepwater horizon oil spill on resident Gulf killifish (Fundulus grandis)

The Deepwater Horizon oil rig disaster resulted in crude oil contamination along the Gulf coast in sensitive estuaries. Toxicity from exposure to crude oil can affect populations of fish that live or breed in oiled habitats as seen following the Exxon Valdez oil spill. In an ongoing study of the effects of Deepwater Horizon crude oil on fish, Gulf killifish (Fundulus grandis) were collected from an oiled site (Grande Terre, LA) and two reference locations (coastal MS and AL) and monitored for measures of exposure to crude oil. Killifish collected from Grande Terre had divergent gene expression in the liver and gill tissue coincident with the arrival of contaminating oil and up-regulation of cytochrome P4501A (CYP1A) protein in gill, liver, intestine, and head kidney for over one year following peak landfall of oil (August 2011) compared to fish collected from reference sites. Furthermore, laboratory exposures of Gulf killifish embryos to field-collected sediments from Grande Terre and Barataria Bay, LA, also resulted in increased CYP1A and developmental abnormalities when exposed to sediments collected from oiled sites compared to exposure to sediments collected from a reference site. These data are predictive of population-level impacts in fish exposed to sediments from oiled locations along the Gulf of Mexico coast. © 2013 American Chemical Society